2/x-2+8/3x-6=7

Solution for 2/x-2+8/3x-6=7 equation:

2/x-2+8/3x-6=7

We move all terms to the left:

2/x-2+8/3x-6-(7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+8/3x-15=0

We calculate fractions


6x/3x^2+8x/3x^2-15=0

We multiply all the terms by the denominator


6x+8x-15*3x^2=0

We add all the numbers together, and all the variables

14x-15*3x^2=0

Wy multiply elements

-45x^2+14x=0

a = -45; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-45)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-45}=\frac{-28}{-90}
=14/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-45}=\frac{0}{-90}
=0
$